Wave-Particle Duality and Smearing

The other day, I thought that matter may perhaps not be confined to particles with a hard edge.  Maybe electrons are more in the form of a 3-D smear instead of a 3-D sphere.  I think that would explain why they have to be located statistically rather than through plain old extrapolation of the classical rules of physics.  And the faster they move, the more they smear.  In some ways a smear may resemble a wave.  Maybe not in all ways, but some.  I like the idea of  a smear more than a string anyway.  I think it makes more intuitive sense.  Also it brings back the old debate about whether matter is continuous and infinitely divisible or not.  Too bad this is just speculation and not a true mathematical model or real life experiment.

Characterism

If I recall correctly, I believe Martin Luther King Jr. stated his wish for a place where a man could be judged by the content of his character.  I guess somebody somewhere would say he had a bigoted viewpoint because he condoned a form of judging.  Rather than being a racist, he was a characterist.  He advocated favorable treatment of those who had good character.  I wish everybody was a characterist.  But sadly, characterism seems to be frowned upon.  I think many people may actually equate it with racism.  What a sad mindset that is.

Easiest Way To Prove Primes Are Infinite

This may be more of an implication than a proof, but I think it's worth sharing because it's so easy to do and may provide a potentially useful algorithm.  Certainly much easier than understanding the traditional proof of the infinitude of the primes in my opinion.

I call it counting by primes.  Was I the first to invent it?  Who knows.

Start with 2 and 3.  Call 2 by the name P1 and 3 by the name P2.

Multiply P1 and P2 in all possible combinations including repetition up to powers of 2.  So you have everything from P1^0 times P2^0 all the way up to P1^2 times P2^2.

So in this case you'd have a combination of numbers like 1 x 2 = 2, 2 x 2 = 4, 3 x 2 = 6, etc.

Look at all the primes you have and all the composites you've generated with those primes.  Generate an entire list, eliminating duplicates.  When you've generated a list, you may see several gaps in between the numbers.  Find the gap in between the lowest values.  In this case, it should be the gap between 4 and 6.  What's the value of the lowest missing number in this gap?  It's 5.  Call 5 by the name P3.

Multiply P1, P2, and P3 in all possible combinations including repetition up to powers of 3.

Look at all the primes you have and all the composites you've generated with those primes (not just in this most recent step, but in all steps of the algorithm thus far).  Generate an entire list, eliminating duplicates.  When you've generated a list, you may see several gaps in between the numbers.  Find the gap in between the lowest values.  In this case, it should be the gap between 6 and 8.  What's the value of the lowest missing number in this gap?  It's 7.  Call 7 by the name P4.

Multiply P1, P2, P3 and P4 in all possible combinations including repetition up to powers of 4.

Wash, rinse, repeat, as I've heard the gamer Aqualung say.  You'll find out that there's nothing to keep you from doing this forever, since even if there was no gap in the list, you could just pick the lowest number you haven't used yet as PN.

If there are typos here, or I messed something up, feel free to criticize.  But I think you can get the general idea and that's what is important.  Perhaps there's a flaw in the idea, but I don't see it.  I'm definitely not the best mathematician.  I remind myself of Winnie-the-Pooh.  A bear of very little brain, but darnit, he likes to try and think.  By the way, did you know Winnie-the-Pooh was created by a guy with a degree in mathematics?